Question

5.3
score: 7/22 answered: 7/22
question 8
find the exact value of the expression.
$\tan ( \frac { 3 } { 4 } \pi ) =$
question help: video ebook message instructor

Explanation:

Step1: Use the tangent formula

We know that \(\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}\), and \(\frac{3\pi}{4}=\pi-\frac{\pi}{4}\). Also, \(\tan(\pi - \alpha)=-\tan\alpha\).

Step2: Calculate \(\tan\frac{\pi}{4}\)

We know that \(\tan\frac{\pi}{4} = 1\).

Step3: Find \(\tan\frac{3\pi}{4}\)

Since \(\tan\frac{3\pi}{4}=\tan(\pi-\frac{\pi}{4})\), and using \(\tan(\pi - \alpha)=-\tan\alpha\), when \(\alpha=\frac{\pi}{4}\), we have \(\tan\frac{3\pi}{4}=-\tan\frac{\pi}{4}\).

Answer:

\(- 1\)